Simplify the following expression: $q = \dfrac{9t^2 - 18t - 315}{t - 7} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $9$ , so we can rewrite the expression: $ q =\dfrac{9(t^2 - 2t - 35)}{t - 7} $ Then we factor the remaining polynomial: $t^2 {-2}t {-35} $ ${-7} + {5} = {-2}$ ${-7} \times {5} = {-35}$ $ (t {-7}) (t + {5}) $ This gives us a factored expression: $\dfrac{9(t {-7}) (t + {5})}{t - 7}$ We can divide the numerator and denominator by $(t + 7)$ on condition that $t \neq 7$ Therefore $q = 9(t + 5); t \neq 7$